Game to arrange groups of tokens spanning an attribute space

ABSTRACT

A game using tokens bearing a number (N&gt;2) of N-valued attributes, by finding, among tokens in each player&#39;s possession alone or in combination with those on a common playing field, groups of N tokens whose attributes, suitably permuted, form lines spanning the N-dimensional cube of N N  combinations, and to arrange the playing field to consist entirely of such groups and networks thereof.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No. 61/207,916, filed Feb. 18, 2009, which is incorporated by reference herein.

BACKGROUND

The present invention relates to a game played by arranging tokens in patterns on a playing field according to rules that pertain to the tokens' attributes.

A well-known example of a game arranging token in patterns on a playing field is dominoes, which is played using a set of tokens called tiles or simply dominoes. Each domino is a block marked with two groups of zero to six dots or “pips” on one surface. Under the basic rules, at each turn, a player attempts to place the end of a domino from his or her hand beside another domino with an end that has a matching number of dots. All the dominoes on the playing field must be connected together. Pips at the ends of lines of tiles are counted with each turn to keep score in some variants of the game, which ends when some team or player has amassed a specified number of points. The public domain describes many details and rules for different games for those interested. More information on dominoes is available at various websites, including http://www.dominorules.com/domino basics.aspx.

Popular as it is, the game of dominoes has some disadvantages. For example, it may become clear that one player's lead is insurmountable well before the end of the game, and kids (among others) may not want to continue a game they are sure to lose. The game of dominoes calls for little or no imaginative or radical problem-solving, in that it prohibits rearrangement of the dominoes after placement on the playing field.

SUMMARY OF THE INVENTION

We recognized and addressed a need for a new game that rewards strategy over chance, can be played in a short time (e.g., a coffee break), holds winning in suspense until the end, and can be easily learned yet challenges players at many different levels.

The present invention is a game played with a set of tokens (e.g., playing tiles) distinguishable by combinations of three or more attributes (i.e., characteristics of interest), each attribute having, on a given token, one of three or more discrete values. The game challenges players to shed all from their hands by (a) identifying playable groups of tokens—groups within which every attribute either (i) retains a single value or (ii) takes on each of its available values—and (b) constructing on a playing field an evolving pattern of tokens, in which (i) every continuous row or column of tokens consists of at least one playable group and (ii) every token belongs to at least one such continuous row or column.

The game is designed for brief and spontaneous play, combining the challenge of recognizing special groups of tokens—among which the several attributes vary maximally or not at all—with the fun of arranging and linking such collections of tokens on a tabletop. Despite the apparent simplicity of its rules, the game rewards subtle reasoning and requires supple visualization.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

FIG. 1 illustrates a first embodiment including instructions, a typical playing tile in perspective view, and a plan view of twenty-seven tiles suitable for use as tokens.

FIG. 2A illustrates some examples of playable groups (in this case, triads) of tiles.

FIG. 2B illustrates examples of non-playable groups (not triads) of tiles.

FIG. 3 is a flowchart to illustrate the sequences of steps used in playing the game.

FIG. 4 is a tabular view of Player A and Player B initially drawing four tiles in a first play-by-play example of the game.

FIG. 5 is a tabular view of a typical lottery to select the player who will start the game.

FIG. 6 is a diagram that illustrates a game opening in which neither Player A nor Player B can build a triad and each must draw a fifth tile in turns 1 and 2.

FIG. 7 is a diagram that illustrates each player building one triad in turns 3 and 4.

FIG. 8 is a diagram that illustrates Player A building a triad and shedding one tile in turn 5, and Player B drawing a tile in turn 6.

FIG. 9 is a diagram that illustrates Player A drawing a tile in turn 7, and Player B building a triad and shedding two tiles in turn 8.

FIG. 10 is a diagram that illustrates Player A winning by shedding his last tiles in turn 9.

FIG. 11 is a diagram that illustrates turns 7 and 8 of an alternate ending, serving as a second play-by-play example, where Player A and Player B have agreed to reveal their tiles and, seeing the tile that Player A has drawn in turn 7, Player B chooses to draw a tile in turn 8 rather than let Player A win as illustrated in FIG. 10.

FIG. 12 is a diagram that illustrates Player A in turn 9 drawing a tile, and Player B in turn 10 completing a square perimeter.

FIG. 13 is a diagram that illustrates Player A in turn 11 drawing a tile by default, and Player B in turn 12 drawing the unique tile that is capable of completing the square.

FIG. 14 is a diagram that illustrates Player A in turn 13 playing a triad as a new island, and Player B starting turn 14 by filling in the square that was framed in turn 10.

FIG. 15 is a diagram that illustrates Player B continuing with turn 14 by trisecting the square into islands and linking the island built in turn 13 to one of the three new islands.

FIG. 16 is a diagram that illustrates Player B finishing turn 14 by shedding the tiles withheld in turn 8, and winning the game by virtue of strategy informed by revealed tiles.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.

The following description includes the best mode of carrying out the invention. This detailed description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is determined by reference to the claims.

The tiles in a first embodiment constitute a set of tokens distinguished by three attributes, each attribute ranging over three values, such that one tile bears each combination of available values of the attributes.

FIG. 1 illustrates the first embodiment of the game, which includes, in addition to an opaque grab bag (not shown), twenty-seven solid tiles (tile 111 through tile 333, with tile 111 shown in both perspective and plan views and the rest in plan view only), and instructions 20. In this first embodiment, each tile bears a marking in one of three shapes (moon, sun, or star) rendered in one of three foreground colors (red, yellow or blue) on one of three background colors (green, violet or orange).

Certain embodiments include rules that permit players to conceal the tokens that they hold. Any of several mechanisms can be used. For example, in the first embodiment the tiles (e.g. tile 111) are constructed with a thickness suitable for standing on edge, and of materials capable of concealing all indicia when viewed from behind (as by opposing players). Other embodiments may include a rack to hold each player's tiles at an angle that facilitates viewing by that player alone.

In the first embodiment, the term “triad” is defined as any group of three tiles in which each attribute (i.e. foreground color, background color, or shape) either retains the same value or takes on all three available values. Thus, taking the shape attribute as an example, in a valid triad, either all three tiles bear the same shape (e.g., all three shapes are moons), or all three tiles bear different shapes (i.e., one moon, one star, and one sun). Similar conditions apply, independently, to the other two attributes.

Players begin the game by drawing the minimum number of tokens (four) that can include a triad without constituting one (which would end the game). With each turn, a player either sheds some tiles from his or her hand by arranging one or more triad(s) on the playing field, or adds a randomly-drawn tile to his or her hand.

FIG. 1 illustrates example instructions 20, including the definition of a triad and the rules, for the first embodiment. The rules are substantially as follows:

-   1. (a) Players agree to reveal or conceal tiles, then each player     draws four tiles;     -   (b) The one with the most red-marked shapes must take his or her         turn first;     -   (c) The first player to run out of tiles will win the game. -   2. During each turn, a player must either (a) shed one or more     tile(s) by building triads on the playing field, or (b) draw a tile     from the grab bag. -   3. Players may freely rearrange triads already on the playing field,     provided     -   (a) every continuous row or column of tiles is a single triad,         and     -   (b) every tile is in some triad disposed as a continuous row or         column.

The game appeals to, and aims to stimulate and challenge, the faculty of visualization, so color plays a natural role in certain embodiments. For example, in the first embodiment, the first two attributes of a tile are foreground and background colors.

The tiles shown in FIG. 1 are assigned three-digit reference numbers. The first digit signifies a foreground color: red (1xx) yellow (2xx) or blue (3xx). The second digit signifies a background color: green (x1x), violet (x2x) or orange (x3x). The third digit signifies a shape: a sun (xx1), a moon (xx2) or a star (xx3). For example, tile 111 is a red-on-green sun, tile 123 is a red-on-violet star, tile 222 is a yellow-on-violet moon and tile 333 is a blue-on-orange star. In alternative embodiments, any three colors (including shades of gray) can be used for the foreground color and any other three colors can be used for the background.

The three-digit reference numbers in the drawings refer to the tiles as follows:

111: red-on-green sun 112: red-on-green moon 113: red-on-green star 121: red-on-violet sun 122: red-on-violet moon 123: red-on-violet star 131: red-on-orange sun 132: red-on-orange moon 133: red-on-orange star 211: yellow-on-green sun 212: yellow-on-green moon 213: yellow-on-green star 221: yellow-on-violet sun 222: yellow-on-violet moon 223: yellow-on-violet star 231: yellow-on-orange sun 232: yellow-on-orange moon 233: yellow-on-orange star 311: blue-on-green sun 312: blue-on-green moon 313: blue-on-green star 321: blue-on-violet sun 322: blue-on-violet moon 323: blue-on-violet star 331: blue-on-orange sun 332: blue-on-orange moon 333: blue-on-orange star

FIG. 2A illustrates a triad 22 in which none of the attributes varies. This can occur in embodiments comprising three complete sets of the twenty-seven tiles shown in the table above. FIG. 2A also illustrates a triad 24 in which one attribute varies (maximally, as it must if it varies at all) among the three tiles, a triad 26 in which two attributes vary, and a triad 28 in which all three attributes vary among the three tiles.

FIG. 2B illustrates several examples of groups of tiles that do not constitute triads. Group 30 is not a triad because an attribute varies incompletely, in that the three tiles have just two foreground colors. Group 32 is not a triad because it has incomplete variation in background color. Group 33 is not a triad because it has incomplete variation in shape. Groups 34 and 36 are not triads because each contains more or less than three tiles.

FIG. 3 is a flowchart illustrating the steps of playing the game. At step 40, the players determine whether the tiles will be revealed or concealed, and each player draws four tiles from a grab bag. FIG. 4 illustrates two players drawing their initial hands (i.e., the collections of tiles in their possession): Player A draws hand 70, consisting of tiles 121, 132, 311 and 322, and Player B draws hand 72 consisting of tiles 112, 323, 113 and 212. The playing field 74 is initially empty.

FIG. 3, in steps 42, 44, 46, 48, 49 and 50, illustrates a method to select the player who will start the game, based on the number of tiles each player holds with a particular attribute value. In the first embodiment, we compare the numbers of tiles bearing a red foreground color. When the players have agreed to reveal tiles at step 40, the “No” branch is taken from decision step 42 to decision step 46, where all the players can see whether some player's initial hand has more red-marked tiles than the other hands or there is a tie. If there is a tie, then every tied player temporarily draws another tile and reveals it at step 48. This lottery proceeds, looping back to decision step 46, until the tie is broken and the “No” branch is taken. When the players have agreed to conceal tiles, the “Yes” branch is taken from decision step 42 and the loop of steps 46 and 48 is preceded by each player temporarily drawing a tile and revealing it at step 44 to determine the starting player. At step 49, any tiles drawn to break a tie are returned to the grab bag. At step 50, the player who showed the greatest number of red-marked tiles is designated the starting player. FIG. 5 is a table representing a possible course of this lottery to determine which player will take the first turn. As shown in tabular form, player A breaks the tie by drawing the red-on-violet star 123, and will have the first turn.

One turn consists of the player's attempt to shed tiles while arranging the playing field to consistent entirely of triads in accordance with rule 3 described earlier. At decision step 52, the player determines if he or she can shed any tile(s). If the player can shed and chooses to shed, following the “Yes” branch of 52 and the “Yes” branch of 54, the player sheds tile(s) at step 56. If this leaves any tiles in the player's hand, taking the “Yes” branch of decision step 58, the player passes the grab bag to the next player at step 62. If the player shed the last tile, the player wins the game at step 64.

At step 62, the player signals completion of his or her turn. This is necessary because the player may rearrange the tiles on the playing field in several steps, any one of which would have satisfied rule 3, as shown in FIGS. 14-16. So, returning to FIG. 3, if the player is left with any tiles (the “Yes” branch of decision step 58), he or she signals completion of the turn by passing the grab bag to the next player at step 62 (or at least touching the grab bag). Interrupting the player's turn by drawing a tile is its own punishment, but trying to shed a tile before the player signals completion of the turn may be discouraged by forcing the interrupting player to draw another tile.

If the player does not shed at least one tile at step 56, whether by choice as in the “No” branch of decision step 54 or by inability as in the “No” branch of decision step 52, he or she must draw one tile from the grab bag in step 60, concluding the player's turn.

Play-by-Play Account of an Example Game with Tiles Concealed by Default

Recapitulating the opening of the example game, we assume that the players have not agreed to reveal tiles (FIG. 3, step 42), and are therefore concealing their tiles from one another. Players A and B draw hands 70 and 72 (FIG. 4). We also assume that Player A is the first to take a turn, by lottery as previously described (FIG. 5). As shown in FIG. 6, Player A, having no triads in her hand, draws tile 231 in turn 1. Player B, having no triads in his hand, draws tile 111 in turn 2. The playing field remains empty.

Tiles newly drawn or shed by either player are shown with heavier borders. Also, in actual play, rows or columns of tiles would be more closely spaced than they appear in the game examples. They are shown with some separation to emphasize their mobility, and for clearer demarcation of groups of tiles such as item 90 in FIG. 12.

FIG. 7 illustrates a case in which the players shed tiles by building triads. In turn 3, Player A sheds tiles 121, 311 and 231 by building triad 80. In turn 4, Player B sheds tiles 112, 113 and 111 by building triad 82.

FIG. 8 illustrates rearrangement of tiles on the playing field to shed a tile. In turn 5, Player A rearranges the tiles of triads 80 and 82 to align tile 231 with tile 113, and sheds tile 322 to link them. The rearranged triads, 84 and 86, are no longer islands, but linked by a triad made of tiles 113, 322 and 231. The corner tiles 113 and 231 are not available for additional connections due to rule 3(a) prohibiting continuous lines of more than three tiles. However, if the linking tile 322 is later moved for use elsewhere on the playing field, the tiles 113 and 231 will be freed as well. This is an advantage to the game as one can freely arrange the tiles on the playing field as long as rule 3 is satisfied. FIG. 8 also shows turn 6, in which Player B sees no opportunity to build a triad and draws tile 312. He can use tile 312 to form a triad, but not until his next turn.

In FIG. 9, turn 7, Player A draws tile 222, observing that the playing field has not changed since her last move. In turn 8, Player B builds the triad 88 downward from triad 86 (FIG. 8), shedding his tile 212 and the recently-drawn tile 312. However, if the players had agreed to reveal tiles in their respective hands, Player B might opt to draw another tile from the grab bag rather than put tile 312 on the playing field, which would seal his fate for the following reason: Player A holds tile 132 and tile 222, which like any pair of tiles uniquely determine which tile would complete a triad. In this case, tile 312 is the very tile Player A needs to have available on the playing field in order to shed her last two tiles.

Player B is unaware of that problem, because the tiles of Player A are concealed by agreement. FIG. 10, turn 9, illustrates the outcome: Player A aligns her tiles 132 and 222 with the tile 312 just played by Player B, emptying her hand and winning the game.

Play-by-Play Account of an Example Game with Tiles Revealed by Agreement

The players in the foregoing game had the option of agreeing in advance to reveal, rather than conceal, their tiles. Supposing this to have been their mutual choice, the game might have ended differently, with strategy playing a stronger role.

FIG. 11 illustrates how turns 7 and 8 might have gone, supposing the same tiles had been drawn and the same moves had been made through turn 6. Player B could have seen that shedding his tile 312 would enable Player A to win. In order to preserve a chance of winning, Player B might have opted to draw another tile from the grab bag at turn 7 rather than provide tile 312 to Player A. Suppose the tile that Player B draws, to avert defeat, is tile 131 (Player A's snarky remarks on the stinginess not shown).

In FIG. 12, Player A next draws a tile 331 in turn 9. Player B rearranges triad 84 (FIG. 11) into triad 90, then sheds tile 131, closing a square of four triads 92 in turn 10.

FIG. 13, turns 11 and 12, illustrate another case where Players A and B cannot see how to build one or more triad(s) and both must draw tiles. They draw tiles 233 and 213, respectively. If Player A doesn't stop him, Player B can use tile 213 in his next turn to transform the square of four triads 92 into a solid three-by-three square of triads.

FIG. 14, turn 13, has Player A shedding tile 132, tile 331, and tile 233 to build an isolated triad 94. Turn 14 begins with Player B filling in the square of triads 95 with the tile 213 drawn in his previous turn. This move illustrates one remarkable result of rule 3: the unique tile that completes the middle row of any given square perimeter of triads is always the same tile that completes the middle column of that square perimeter.

FIG. 15 illustrates that a player who completes a solid square creates multiple possibilities for the former corner tiles to form new connections. Turn 14 continues with Player B separating the square of triads 95 (FIG. 14) into three triads 96, 98 and 99, and shedding tile 323 to link the former corner tile 113 to tile 233.

In FIG. 16, turn 14 ends with Player B shedding tiles 212 and 312 by combining them with tile 112 to form a triad, emptying his hand, and winning the game.

Some Consequences of the Rules of the Preferred Embodiment

Rule 3 permits tiles to be built on the playing field in “islands” (isolated triads) such as triad 80 and triad 82 shown in FIG. 7, in chains as shown in FIG. 11, in networks as shown in FIG. 9, in 3×3 square perimeters such as triad 92 in FIG. 12, or in solid 3×3 squares such as triad 95 in FIG. 14, and in some other configurations combining these.

As an unexpected result of Rule 3, illustrated in FIG. 14 and noted above, when eight tiles form a square perimeter of four triads (each corner tile belonging to two triads), the single tile that would be required in order to complete a triad with the middle tiles in any two opposite sides of this square is always identical with the tile that would complete a triad joining the middle tiles of the other two sides, whence such an empty square can always be filled in by some particular tile. (Diagonals of such a square do not generally form triads, and they don't have to, because rule 3(a) only requires continuous rows or columns of tokens to consist of triads.) The resulting solid square can be trisected, that is, sliced into three triads, either horizontally or vertically, presenting various possibilities for former corner tiles to make new connections. Since the opposing player(s) will have similar possibilities at their disposal, such a move may be best reserved for the last turn.

Certain Alternative Embodiments

The above embodiment is one of a family of games within the ambit of the invention, each game using a set of tiles or tokens bearing a number (N>2) of N-valued attributes. The number of distinct tokens needed to cover all the combinations is (number of values) raised to the power (number of attributes), or N^(N), hence the number of tokens is at least 3³=27. For a given value of N, a “playable group” is defined as a group of N tokens in which each attribute either retains a single value or takes on all N allowed values. With this general notion of a “playable group” (which includes a “triad”), the generalized rules become:

-   1. (a) Players agree to reveal or conceal tiles, then each player     draws N+1 tiles;     -   (b) The starting player is selected by lottery or by agreement;     -   (c) The first player to run out of tokens will win the game. -   2. During each of their turns, players must either:     -   (a) use up some of their own tokens by building playable groups         on the table, or     -   (b) draw a token at random from the grab bag. -   3. Players may freely rearrange playable groups already on the     table, provided     -   (a) every continuous row or column of two or more tokens         consists of a playable group; and     -   (b) every token is in some playable group disposed as a         continuous row or column.

With the number of attributes (and of values) N=4, there would be 4⁴=256 tokens, corresponding directly to bytes. This variant of the rules would be especially amenable to embodiment in a computing device. The attributes in this case would be fields of two bits within a byte, each bit field admitting of 4 values. Larger values of N are also conceivable although it would entail at least 5⁵=3,125 tokens.

The choice of attributes for the tokens is arbitrary, to such an extent that the tokens themselves, as well as the playing field and the hands of one or more players, may in some embodiments appear only as images displayed by one or more computing devices. The game-playing apparatus embodying the invention in such cases would consist of a computing device including a processor executing a program designed to supervise the execution of externally-supplied software algorithms and to verify their conformance to the rules disclosed here. The supervisory program would enable such software algorithms to play against one another, in addition to or instead of one or more humans. In several embodiments, the software is implemented on a computing device such as a PC, an Apple computer, an Apple iPhone, or a Web application.

Thus the game-playing apparatus may comprise a computing device programmed to execute competing game-playing algorithms or accept commands from competing agents. The playing field and players' hands would exist in the memory of the computing device and could also be depicted in a computer display. Play would be controlled by (i) one or more human players, or (ii) one or more instances of competing algorithms programs, or (iii) agents of both types.

Other embodiments of the game, suitable for more than four players, are readily derived by combining multiple sets of tokens.

The first embodiment includes an opaque grab bag of suitable size and design (not shown) to store all the tiles, mix them up, and manually remove them individually during a game. Such a grab bag, while not essential to the invention, is an element of that embodiment because it serves both as a way to identify the current player and as a convenient package for the tiles. Any suitable shuffling or randomizing dispenser could substitute for the grab bag.

The instructions 20 in FIG. 1, taking a geometrical approach to explain the concept of a triad, indicate that the tiles could be arranged by their attributes to form a 3×3×3 block or “cube.” For example, one could construct the cube by stacking or layering the 3×3 square of nine tiles (x1x) with a green background atop the nine tiles (x2x) with a purple background, which are stacked atop the nine tiles (x3x) with an orange background. The instructions 20 define a “triad” as a set of three tiles that would form a straight line in any direction, even diagonally, through such a “cube” of attributes. In some alternative embodiments, rules may prohibit space diagonals and/or plane diagonals. Prohibiting space diagonals would mean that at least one attribute would have to be held constant; prohibiting plane diagonals as well would mean that only one attribute could vary (maximally, if at all) in a valid triad.

Rule 3(a) effectively limits the number of playable groups that can share a given token to two. We have found that requiring every continuous row or column of tokens to be a single playable group does not unduly limit possible moves so much as it forces us to search more deeply for available moves than if playable groups could extend in all four directions from one tile. However, in some embodiments, the rule may be dropped, so that a tile can belong to up to four playable groups. Even in such cases, every continuous row or column of two or more tokens must consist of one or more playable groups.

All three (or N) attributes may be freely chosen, while preserving the challenge of constructing networks of playable groups of tokens on a playing field. For example, the length, width and depth of the token could be used as attributes, or the shape of the token itself, its surface texture, and its consistency could form an alternative, tactile attribute space. The attribute of shape need not be used, but if it is, numerous alternatives exist, such as squares, circles and triangles, or depictions of planes, trains and automobiles. In other embodiments, background color could be replaced by other attributes such as number of markings as described in U.S. Provisional Application No. 61/207,916, or surface finish (e.g. glossy, matte, rough) or material (e.g. wood, metal, stone). 

1. A game-playing apparatus, comprising: (A) a set of at least twenty-seven tokens distinguishable by a number of attributes, each attribute ranging over an equal number of values, including at least one token bearing each combination of said values, labelled or accompanied by (B) rules requiring each player in succession (i) either to (a) find, among tokens in said player's possession alone or in combination with those previously placed on a common playing field, one or more groups, herein designated “playable groups” to signify that among any such group, each attribute independently either retains a single value or takes on all of its available values, and (b) construct on a common playing field, by a process including the shedding of at least one of said player's tokens and permitting manipulation of tokens already on said field, an arrangement of tokens in which (1) every continuous row or column of two or more tokens consists of at least one playable group, and (2) every token lies in at least one playable group thus disposed, (ii) or to draw one token at random from the remaining pool.
 2. The game-playing apparatus of claim 1, wherein said rules specify that the tokens must be disposed on said field in such a way that (A) every continuous row or column of two or more tokens consists of exactly one playable group, and (B) every token belongs to at least one such continuous row or column.
 3. The game-playing apparatus of claim 2, wherein a game is defined to (A) begin with the drawing of a fixed starting number of tokens at random from a pool by each player, and (B) end with the victory of the first player to run out of tiles.
 4. The game-playing apparatus of claim 3, wherein the rules are enforced by a computing device programmed to execute game-playing algorithms, and (A) the playing field is in a computer display, and (B) said display depicts arrangements of tokens currently in play and groups of tokens held by one or more players, as controlled by (i) one or more human players, or (ii) one or more instances of competing software programs, or (iii) playing agents of both types.
 5. A game-playing apparatus, comprising: (A) a set of at least one complement of twenty-seven tokens, each bearing a single marking of one of three distinct shapes, printed or displayed as a foreground in one of three distinct colors, on a background printed or displayed in one of three other distinct colors, each such complement of tokens containing one token bearing each combination of marking shape, foreground color and background color, and (B) labelling specifying rules requiring each player in succession (i) either to (a) find, among tokens in said player's possession alone or in combination with tokens previously placed on a common playing field, one or more special groups, herein termed “triads,” consisting of three tokens, each bearing a marking, such that all three of the markings either match or differ in shape, in color and in background color, and (b) construct on a common playing field, by a process including the shedding of at least one of said player's tokens and permitting manipulation of tokens already on said field, an arrangement of tokens in which (1) every continuous row or column of two or more tokens consists of at least one triad, and (2) every token lies in at least one triad thus disposed, (ii) or to draw one token at random from the remaining pool.
 6. The game-playing apparatus of claim 5, wherein said rules specify that the tokens must be disposed on said field in such a way that (A) every continuous row or column of two or more tokens consists of exactly one triad, and (B) every token belongs to at least one such continuous row or column.
 7. The game-playing apparatus of claim 6, wherein a game is defined to (A) begin with the drawing of a fixed starting number of tokens at random from a pool by each player, and (B) end with the victory of the first player to run out of tiles.
 8. The game-playing apparatus of claim 7, wherein the rules are enforced by a computing device programmed to execute game-playing algorithms, and (A) the playing field is in a computer display, and (B) said display depicts arrangements of tokens currently in play and groups of tokens held by one or more players, as controlled by (i) one or more human players, or (ii) one or more instances of competing software programs, or (iii) playing agents of both types. 